Presented at AMEMR 2008, Plymouth, UK

MULTI-ELEMENT ECOSYSTEM DYNAMICS IN THE SERIES
IRON-ENRICHMENT EXPERIMENT:
COMPARING OPTIMAL UPTAKE KINETICS
TO MICHAELIS-MENTEN
1 2 1
S. Lan Smith , Naoki Yoshie , Yasuhiro Yamanaka
1
Ecosystem Change Research Program,
FRCGC, JAMSTEC, Yokohama, Japan
2
Tohoku National Fisheries Res. Inst., Shiogama, Japan

Outline
Introduction to SERIES
Model Introduction
Brief Review of Nutrient Uptake kinetics
Results & Conclusions

S. Lan Smith, FRCGC, JAMSTEC AMEMR Symposium, June, 2008

SERIES Expt. Changes in Growth Rate & Si:N ratio
Fe Stress
Iron-fertilization Expt. 0.5 (A)

in the NE subarctic Pacific Specific 0.4
Growth 0.3
Rate 0.2
Takeda et al (2006, DSR II 53) (d−1) 0.1
modeled it using a modified 0.0
version of the NEMURO model (B)
1.0

Nutrient 0.8 [Si(OH)4]

NEMURO assumes fixed ratios [NO3-]

Drawdown 0.6
e.g., N:Si, C:N
(μmol L−1 d−1) 0.4
They applied two Si:N ratios 0.2

for diatoms 0.0

Fe-replete: Si:N = 1 Si: N (C)
3.0
Fe-stress: Si:N = 3 Drawdown
2.0
Ratio
Switching was based on
(mol: mol) 1.0
degree of Nutrient limitation
0.0
=> Added 2 parameters to NEMURO 0 5 10 15 20 25
Time (days)

S. Lan Smith, FRCGC ECRP

Si:N Uptake ratios and Iron Fertilization
Iron Fertilization
Si:N Uptake Rates Decrease because of Faster DIN uptake
Franck et al. (DSRII 47, 2000), Franck et al. (MEPS 252, 2003)
Iron Limitation
Even Moderate Iron Stress can Increase Si:N Uptake Ratio,
e.g., in ship-board expts., Southern Ocean:
Si:N uptake increased for DFe < 0.5 nM, even though KsFe < 0.2 nM
Franck et al. (DSRII 47, 2000)
in SERIES
Around the transition from Iron-replete to Iron-limiting,
BSi-specific Si Uptake Rate increased &
Si:N Uptake Ratio increased,
but NOT because of a decrease in DIN uptake, as in bottle expts.
Boyd et al. (L&O 50, 2005)


Variable Composition Ecosystem Model: QeNEMURO

DIN Fe DSi
Uptake
PS = non-diatoms Excretion
N quota only
PL
PS Grazing
PL = diatoms
N, Fe & Si quotas Sloppy
Feeding
ZS, ZL & ZP
ZS ZL
fixed C:N, Fe:N ratios Decay/
only N biomass calc'd remineralization
ZP
N-based growth eff.
Mortality
Similar to the model of Smith
Egestion
et al. J. Mar. Sys. 64, 2007

Detr. DOM
S. Lan Smith, FRCGC, JAMSTEC June, 2008

Nutrient Limitation: Droop's Quota model + Fe-limited α
q0i
Growth Rate, µ = µinf L min (1 − )
Qi
i
µ
Qi is cell quota of nutrient i
0
for diatoms: i = N, Si, Fe Q
q0i
Parameters:
µinf = Growth Rate at Infinite Cell Quota
q0i = minimum or quot;subsistencequot; cell quota for nutrient i

Light Limitation: L = (1 − e−αI / µinf )
q0Fe
α depends on Fe: α = α0 (1 − )
QFe
i.e., iron limitation reduces α,
similar to Chai et al (GBC 21, 2007), based on iron-fertilization expts.
(Lindley et al, DSRII 42, 1995; Lindley and Barber, DSRII 45, 1998).

Modeling Dissolved Iron

A fixed time-series of
dissolved iron was applied,
as fit to the data by
Takeda et al (2005).
Unknown Losses of Fe
0 5 10 15 20 25
(e.g., scavenging & sinking) Time (Days)
=>
Fig. 3A from Takeda et al (DSRII 53, 2006)
This is preferable to
a prognostic equation for iron.


Rate Expressions for Nutrient Uptake
Michaelis-Menten (MM) Equation
Vmax S U
Uptake Rate, U(S) = [ K + S ] S
s

Affinity-based Equation (Aksnes & Egge, MEPS, 1991)
1 More general
V(S) = [ (A S)−1 + (V )−1 ] Reduces to MM as a special case
s max

Optimal Uptake (OU) Equation (Pahlow, MEPS, 2005) Both are
mostly protein
Uptake Sites more sites => Greater Affinity, A (lower Ks)
& contain
Internal Enzymes more enzymes => Greater Vmax lots of N.

fA = fractional allocation
Cell
Ion Channels
= Uptake Sites
of internal N:
A = A0 fA
Nutrient Internal
Vmax= V0 (1 − fA)
Ions Enzymes

Acclimation
Low Nutrient Conc. High Nutrient Conc.

Essence of the SPONGE: Dynamic Physiology for Efficient Nutrient Uptake

Assume a fixed total amount of internal N for Uptake Hardware
Phytoplankton maximize uptake of the growth-limiting nutrient,
without reference to concentrations of non-limiting nutrients.
They allocate N for uptake hardware
in the same proportion for all nutrients
based only on the concentration of the growth-limiting nutrient.

Low Nutrient Concentration High Nutrient Concentration
for two
Uptake Sites nutrients,
Cell Cell
& ,
each with
Nutrient
its own
Enzymes
Ions
set of
uptake sites
& enzymes
Many uptake sites, few enzymes Few uptake sites, many enzymes

Simple Phytoplankton Optimal Nutrient Gathering Equations (SPONGE)

Optimize only for Limiting nutrient, L with conc. SL
Pahlow's single-nutrient Optimal Uptake Equations:
1 1
VLim = fA =
]−1 + [fAA0, LSL]−1 1/2
[(1−fA)V0, L A0, LSL
( ) +1
V0, L
for any Non-Limiting Nutrient, n with conc. Sn
Vnon = f (Sn, SL)
=> Sub-optimal uptake of Non-limiting nutrients
1
Vnon= fA = same as above
[(1−fA)V0, n ]−1 + [fAA0, nSn]−1

NOTE: Limiting Nutrient is determined by the Quota model,
NOT directly by uptake parameters.

S. Lan Smith, ECRP, FRCGC AMEMR, June, 2008

Reducing the SPONGE to MM Kinetics

for Limiting nutrient, L with conc. SL
Pahlow's single-nutrient Optimal Uptake Equations:
1 1
Set fA = constant
VLim = fA =
[(1−fA)V0, L ]−1 + [fAA0, LSL]−1 A0, LSL 1/2 + 1
( )
(NO Acclimation)
V 0, L
for any Non-Limiting Nutrient, n with conc. Sn Vnon = f (Sn, SL)
Affinity-based kinetics
with constant params.
1 is the same as above
f = same as MM.
Vnon=
[(1−fA)V0, n ]−1 + [fAA0, nSn]−1 A
(Aksnes & Egge, 1991)


1. Two versions of the model: SPONGE & MM uptake kinetics
Fit each to all data INSIDE Iron-fertilized patch:
2. Compare fits & modeled material flows, composition

Fitting Method
Markov Chain Monte Carlo (MCMC)
as applied by Smith et al. (J. Mar. Sys. 64, 2007), Smith and Yamanaka (L&O 54,
2007; Ecol. Model., 2007), Hargreaves and Annan (Climate Dynamics 19, 2002)
+ Penalty (added to cost function) for Unrealistic N:C cell quotas > 0.25

Parameters Varied (determined by fitting)
chosen iteratively, based on Assimilations & Sensitivity Analyses
Growth Rate (at infinite cell quotas) 1
Nutrient Uptake Rate Parameters 9
Grazing Rate (Zoo grazing diatoms) 1
total no. 10


Comparing Best-fits to IN-Patch Data
Two versions of the model, Fits are very
identical except for uptake kinetics: similar. 10
Nitrate
MM version SPONGE version
µM 5 NH4
best costs: 44.7 44.1
0
The model is
Specific Growth Rate Slight
0-D (Mixed- 15 SiOH4
of diatoms differences
layer only). 10
for Growth µM
Vertical bars are 5
0.4
Rates.
Std. Deviations 0
0.3
as assumed
(day-1)

With SPONGE,
for weights Chl
0.2 6
sudden changes
in the fitting. µg/L 4
when limiting
0.1
Data are 2
nutrient
assumed to be 0.0 0
switches.
averages over 0 10 20 0 10 20
Å@
the mixed-layer. Time (days) Time (Days)

Steep, Synchronous Changes
Specific Growth Rate
Limiting
Growth Rate & Si:N drawdown ratio N Fe
Nutrient
Neither version of the model can reproduce 0.4
the change in Growth Rate. 0.3

(day-1)
Both versions reproduce the steep change in Si:N, 0.2
through changing the proportion of diatoms.
0.1
An NPZD model (only diatoms) could NOT.
0.0
Diatoms as a fraction MM version
of total phytoplankton (N) 3
SPONGE version

Si:N (mol:mol)
1.0
0.8 2
0.6
0.4 1
0.2 Data for drawdown ratio
from Takeda et al (1996)
0.0 0
were corrected for Patch
0 10 20 0 10 20
dilution, but model was not.
Time (Days) Time (days)

Increase in Si Uptake Rate at onset of Iron Limitation

BSi-Specific Si Uptake Rate
Limiting
N Fe
Nutrient 0.3

mol (mol BSi d)−1
SPONGE yields an increase
0.2
at the transition to Fe-limiation.
MM kinetics predicts a decrease. 0.1
Both models overestimate the observed rates, 0.0
but SPONGE agrees with the trend. 0.3
Time Means of modeled rates: 0.2
Obs. from Boyd et al. (L&O 50, 2005) 0.1

0.0
Switch from N- to Fe- limitation in models: 5 15 25
Å@
SPONGE: day 12-13
MM: day 16-17 Time (Days)
Boyd et al. (L&O 50, 2005) estimated day 12
from Observations


C-specific Rates of Nutrient Uptake (per mol C biomass)
Limiting N Fe
Nutrient 60

µmol (mol C d)−1
Compared to Michaelis-Menten,
40
SPONGE takes up

Fe
20
growth-limiting nutrient faster
0
non-limiting nutrients slower
0.10
Uptake rates of ALL nutrients depend 0.08
on the conc. of growth-limiting nutrient. 0.06

N
mol (mol C d)−1
0.04
Si uptake rates change sharply, even 0.02
though it never becomes growth-limiting. 0.0
0.6
0.4
Switch from N- to Fe- limitation in models:

Si
0.2
SPONGE: day 12-13
MM: day 16-17
0.0
Boyd et al. (L&O 50, 2005) estimated day 12
0 10 20
Å@
from Observations
Time (Days)


Modeled Cell Quotas of Nutrients for Diatoms
Limiting N Fe
Nutrient 120

nmol (mol)−1
MM kinetics predicts a much higher 80

Fe:C
peak Fe : C ratio. 40
SPONGE suppresses uptake of 0
non-limiting nutrients. 0.25

µmol (mol)−1
(Smith & Yamanaka, L&O 52, 2007)

N:C
0.15
Differences in N : C ratio of diatoms
0.05
cause differences in Zooplankton biomass: 0.0
food quality effect

µmol (mol)−1
2.0
Mitra et al. (L&O 52, 2007) 1.5

Si:C
Grazing is based on C biomass 1.0
0.5
of prey as suggested by Mitra et al. (L&O 52, 2007)
0.0
0 10 20
Å@
Time (Days)

Modeled Biomass of Zooplankton

MM version SPONGE version 0.12

µmol N L−1
0.08
Great Differences in Small and Large Zoo. ZS
0.04
ZL are the main grazers of diatoms.
0.0
ZP also graze diatoms.
0.5

µmol N L−1
ZL
0.4
Results from different N : C quotas of diatoms 0.3
with SPONGE vs. OU kinetics. 0.2
0.1
0.0

0.04

µmol N L−1
0.03
ZP
0.02
0.01
0.0
0 10 20
Å@

Time (Days)


Conclusions
The model reproduces the steep change in Si:N drawdown ratio
mostly through changing the proportion of diatoms.
using either MM or SPONGE utpake kinetics,
even without an increase in Si:N uptake ratio (MM version).
Takada et al (2006) did say this quot;floristic shift could not be ruled outquot;.
SPONGE yields different dynamics than MM:
Sharp changes in uptake rates when the limiting nutrient changes,
Si uptake Rate increases, which agrees with observations,
(whereas MM does not).
Sudden, yet small, changes in Growth Rates.
Large Differences in phy. cell quotas & Zooplankton Biomass.
Yet neither version of the model can reproduce the steep
change in Growth Rate.
A Simpler NPZDD-quota model could not, either.
So, what is missing ? ... other energetic requirments (e.g., for Chl) ?

Modeled Rates of Nutrient Uptake by Diatoms (per L water)

25

10−12 mol L−1 d−1
Steep Changes
MM version Fe
SPONGE version with SPONGE
15
because of
optimization 5
0
with respect to
growth-limiting
0.3 N
nutrient,
0.2
Si : N Uptake Ratio
which cause
of diatoms 0.1

µmol L−1 d−1
steep changes
0.0
15 in Uptake Ratio.
(mol:mol)

Si
1.5
10
1.0
5
0.5
0 0.0
0 10 20
0 10 20 Å@

Time (days) Time (Days)


Presented at AMEMR 2008, Plymouth, UK

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Presented at AMEMR 2008, Plymouth, UK